Inspired by new signing Jean-Ricner Bellegarde and the energetic Pedro Neto, Wolves took the lead after seven minutes when Hwang Hee-chan finished off a brilliant solo run from Neto.
Wolves dominated the first half but missed glorious chances to add to their lead, before Cody Gakpo equalised 10 minutes into the second half.
Liverpool were on top for almost every minute of the second half and finally took the lead after 85 minutes when Andy Robertson arrived in the box to finish.
To add more pain to Wolves’ defeat, substitute Hugo Bueno was credited with an own goal following Harvey Elliott's strike to add a third, as Wolves fell to defeat.
Gary O’Neil made two changes to his side and switched to a 4-3-3 formation.
Bellegarde made his debut and came in alongside Hwang, as Pablo Sarabia and Fabio Silva dropped to the bench.
For Liverpool, Trent Alexander-Arnold and Virgil van Dijk were missing, as 20-year-old centre-back Jarell Quansah made his first start for the club.
Bellegarde, and Wolves, made an excellent start to the game as they pressed Liverpool into submission.
But it was a superb solo run from Neto that put Wolves ahead. He danced inside Joe Gomez and beyond Joel Matip to put in a low cross, which Hwang met at the far post to turn home.
Wolves were all over Liverpool in the opening minutes as Neto and Bellegarde also came close to doubling the lead.
Liverpool settled after the Wolves onslaught and began enjoying more possession, but the hosts defended well and were looking for counter-attacking opportunities, with Neto looking particularly dangerous.
Wolves responded with a spell of pressure themselves and should have made it 2-0 with a free header. Neto nutmegged Gomez and crossed for Matheus Cunha, but he mis-timed his jump and saw the ball bounce off his chest and to safety.
Gakpo had a couple chances for Liverpool, before Jose Sa dropped a cross and handed Mohamed Salah a chance. Mario Lemina made a superb block before Sa made an excellent follow-up save.
Despite that chance, Wolves were good value for their lead as they entered the break winning 1-0.
Liverpool dominated the opening 10 minutes of the second half as they penned Wolves back, before eventually finding their equaliser. Salah was found on the right flank and put in a low cross that allowed Gakpo to finish at the far post.
The visitors continued to dominate and Max Kilman made a superb block to deny a certain Darwin Nunez goal, as Wolves hung on.
After 77 minutes, O’Neil brought on Tommy Doyle for his debut, alongside Boubacar Traore, as Wolves looked to regain some more control in midfield.
Liverpool’s pressure finally came off in the 85th minute when they took the lead. Salah on the right again crossed low and Robertson snuck inside to finish beyond Sa, who did not cover himself in glory as the ball went under him at his near post. The goalkeeper also handed the ball to Robertson with a poor long kick in the build up to the goal.
Bueno was unfortunate to concede from Elliott's shot to make it 3-1 in added time, to add insult to injury for Wolves.
Wolves slumped in the final minutes as they waited for the final whistle to confirm their fate, as they made it four losses from the opening five league games.
GOAL 7 Hwang puts Wolves ahead
GOAL 55 Gakpo equalises for the visitors
GOAL 85 Robertson wins it for Liverpool
GOAL 91 Elliott makes it 3-1
Wolves: Sa, Semedo, Dawson, Kilman, Ait-Nouri (H.Bueno, 65), Gomes, Lemina (Traore, 77), Bellegarde (Doyle, 77), Neto, Cunha (Silva, 60), Hwang (Doherty, 60).
Subs not used: Bentley, Toti, Sarabia, Kalajdzic.
Liverpool: Alisson, Gomez, Matip, Quansah (Konate, 82), Robertson, Szoboszlai, Mac Allister (Diaz, 45), Jones, Salah (Gravenberch, 93), Jota (Elliott, 56), Gakpo (Nunez, 56).
Subs not used: Kelleher, Tsimikas, Bajcetic, Endo.